why are there 360 degrees in a circle, why not 100?

http://en.wikipedia.org/wiki/Degree_(angle)

Well the definitive answer to that is shrouded by the mists of time (goes back further than existing records).

It would be logical to assume that the motions of the sun, moon, and planets were the basis for this. It was important for agriculture to know when to plant and harvest for optimizing results, for one thing. The development of geometry would naturally coincide with this and circles were the best graphics to use for describing those observed cycles. It all just fits together (for early astronomy).

The fact that many star names appear in Sumerian suggests a continuity reaching into the Early Bronze Age. Sumerians used a sexagesimal (base 60) place-value number system, which simplified the task of recording very large and very small numbers. The modern practice of dividing a circle into 360 degrees, of 60 minutes each, began with the Sumerians, undoubtedly based on their observations of the movements of the Earth, sun, and moon.

Those origins are inextricably related to the seasons being determined to be 4, and each season 3 months. That gives 12 months. 30 days per month from the lunar calendar for 12 months gave 360 distinct positions of sun, moon and earth.

In 46 BC Julius Caesar instigated calendar reform and adopted a calendar based upon the 365 1/4 day year length originally proposed by 4th century BC Greek astronomer Callippus.

Wow! What a great question. Thanks for asking it 'cause it made me look into it and I was surprised by the answer -- I honestly thought it 'had' to be 360 due to something to do with pi or some other constant but it is apparently arbitrary. Here ya go:

The original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year.[2] Ancient astronomers noticed that the sun, that follows through the ecliptic path over the course of the year, seems to advance in that path by approximately one degree, each day. Some ancient calendars, such as the Persian calendar, used 360 days for a year.

they made it in reference to how many days the earth took to go "circle" the sun

Because thats not how degrees work.